Problem: Complete the recursive formula of the geometric sequence $27\,,-9\,,\,3\,,-1,...$. $b(1)=$
Solution: The first term is $27$ and the common ratio is $-\dfrac13$. ${\times\left(-\dfrac13\right)\,\curvearrowright}$ ${\times\left(-\dfrac13\right)\,\curvearrowright}$ ${\times\left(-\dfrac13\right)\,\curvearrowright}$ $27,$ $-9,$ $3,$ $-1,...$ This is the recursive formula of $27\,,-9\,,\,3\,,-1,...$. $\begin{cases} b(1)=27 \\\\ b(n)=b(n-1)\cdot\left(-\dfrac13\right) \end{cases}$